Ratio of lateral contraction to axial extension under load.
When a bar stretches axially, it contracts laterally: ν=-ε_lat/ε_axial, typically 0.25–0.35 for metals and about 0.5 for rubber (incompressible). Relations G=E/(2(1+ν)) connect elastic constants.
A rod of ν=0.3 stretched by 0.1% narrows by 0.03%.
Poisson's ratio explains why a stretched bar gets thinner, which affects pressure vessels, fasteners and composite design.
Ratio of lateral contraction to axial extension under load.
Poisson's ratio explains why a stretched bar gets thinner, which affects pressure vessels, fasteners and composite design.
Metals are usually around 0.3, while rubbers approach 0.5 for near-incompressible behaviour, and it cannot exceed 0.5 for an isotropic material.
Constrained lateral strain creates additional stresses in the walls, so the biaxial state must be included in the design.
Typical applications include estimating the change in diameter of a steel tube under tension, calculating the stress state of a thick-walled cylinder under pressure and predicting how a bolt shank narrows when preloaded.
Study "Young's modulus" first (topic 47 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Dimensionless. Range -1 to 0.5 for isotropic materials. Cork has ν≈0.
A rod of ν=0.3 stretched by 0.1% narrows by 0.03%.
The next topic is "Axial deformation", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 48 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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